Problem: Multiply the following complex numbers: $({1-4i}) \cdot ({-1-5i})$
Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({1-4i}) \cdot ({-1-5i}) = $ $ ({1} \cdot {-1}) + ({1} \cdot {-5}i) + ({-4}i \cdot {-1}) + ({-4}i \cdot {-5}i) $ Then simplify the terms: $ (-1) + (-5i) + (4i) + (20 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ -1 + (-5 + 4)i + 20i^2 $ After we plug in $i^2 = -1$ , the result becomes $ -1 + (-5 + 4)i - 20 $ The result is simplified: $ (-1 - 20) + (-1i) = -21-i $